This is comparable to the invariance under spatial translation
that visual object recognition systems seek to achieve.
In that case, categorisation should be driven purely
by the shape of an object and not by the position
it occurred in during training.
Convolutional architectures address this by combining
convolutional layers, which are equivariant under translations,
with pooling layers, which are invariant under translations.In fact, as described in Appendix , the architectures applied in practice to image recognition tasks often fall short of full translation in variance [1]}, [2]}, [3]}.
Specifically, the output of a pooling function,
\(y=p(x)\)  remains unchanged when the input, \(x\) ,
is translated within its receptive field:
\(p(x)=p(Tx)\) .
Commonly, a fixed pooling function,
such as maximum or average, is used to combine the signals
across a range of positions, creating larger receptive fields,
which then feed into the next convolutional layer,
until a final global pooling layer is applied
across the whole image.
That is, in simple terms, a convolutional layer
produces a feature for every position in the input
and a global pooling layer aggregates these features
to give a single position independent output.
